Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-8x+6y &= 6 \\ -4x+8y &= -2\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-4x = -8y-2$ Divide both sides by $-4$ to isolate $x$ $x = {2y + \dfrac{1}{2}}$ Substitute this expression for $x$ in the first equation. $-8({2y + \dfrac{1}{2}}) + 6y = 6$ $-16y - 4 + 6y = 6$ Simplify by combining terms, then solve for $y$ $-10y - 4 = 6$ $-10y = 10$ $y = -1$ Substitute $-1$ for $y$ in the top equation. $-8x+6( -1) = 6$ $-8x-6 = 6$ $-8x = 12$ $x = -\dfrac{3}{2}$ The solution is $\enspace x = -\dfrac{3}{2}, \enspace y = -1$.